It has been known to drive the agricultural vehicle at any selected speed by means of a speed change lever, with a possibility that said vehicle could be controlled to change its path of advance by means of a steering wheel. In the prior art of this type, the right and left crawlers receive traction forces through respective belt- or hydraulic-reduction apparatuses controlled by the speed change lever in a step-less manner. A differential gearing is also involved to be controlled by a step-less speed reducer that in turn is operated by the steering wheel so as to smoothly change the difference in rotational speed between the right and left crawlers. If only the steering wheel is operated, movement speed of the vehicle would remain almost constant during its straight advance and its turning motion. Thus, it has been necessary for drivers of those vehicles to lower the running speed thereof when causing them to make a ‘spinning turn’ of a relatively small radius. In other words, those drivers have had to quickly maneuver both the steering wheel and speed change lever in order to make a turn at an end bare area in any farm. It has also been known to automatically lower the travelling speed of the vehicle in response to the maneuvering of its steering wheel. In this case, the speed will be raised also automatically when said steering wheel is operated to resume the vehicle's straight running. Any troublesome operations for speed change of the vehicle will no longer be required even when the steering wheel is operated to cause the vehicle to make a spinning turn. However, such a system has proved problematic or disadvantageous in that the vehicle speed would unintentionally be reduced even during the vehicle's works free from any spinning motion. In this event, operation efficiency would be impaired and such an unwanted speed reduction in a wet farm would cause therein a non-smooth or unreliable advance of the vehicle. The steering mechanism may be designed such that rotation of the steering wheel brings about a lesser change in vehicle speed. Such a modification also is unsatisfactory because the vehicle will not be able to make a quick turn on road on one hand and a spinning turn in dry farms.